When changing bevel on curves, the curves disappear
For each point in a curve you can specify a radius, this value alters the radius of the bevel at that point of the curve. When a point has a radius of 0.0 there is no bevel at that point (or between two points of zero radius). While selected in object mode the curve is highlighted along the zero size area but deselecting it will hide that section.

Here we have a deselected curve with bevel.



Selecting the curve highlights an extra part that wasn't visible.



In edit mode you can see the radius value in the properties sidebar. You can also use AltS to adjust the radius in edit mode.